Question: 21. Let VI ' v be independently distributed as N(O, 1), and given VI = VI ' v = Vn , let

21. Let VI" ' " v" be independently distributed as N(O, 1), and given VI = VI " ' " v" = Vn , let X; (i = 1, .. . , n) be independently distributed as N(8vj ,1). (i) There does not exist a UMP test of H : 8 = 0 against K : 8 > O. (ii) There does exist a UMP conditional test of H against K given the ancillary (VI" .. , v,,).

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